These demonstrations are provided as Quicktime movies, which can be downloaded or viewed directly in most web-browsers. (To download a free Quicktime player, go here.) These movies are a bit large and choppy, but they should be sufficient to illustrate the basic manipulations. If you have any trouble viewing the movies, downloading them and then playing them from your local hard-drive may help. As highly compressed versions of the original stimuli constructed for demonstration purposes, these movies may not preserve the precise spatial and temporal characteristics of the originals.

Our visual environment contains too much information for us to fully process, and so the visual system has the ability to quickly summarize visual scenes in various ways -- e.g. efficiently extracting the average value of a visual dimension, such as the average size of a group of discs. Existing work on such statistical summary representations (SSRs) has always used discrete input -- either spatial arrays of shapes, or temporal sequences of shapes presented one at a time. Real-world visual environments, in contrast, are intrinsically continuous and dynamic. To better understand how SSRs may operate in natural environments, we investigated the ability to compute average size in visual displays wherein the objects (or sometimes a single object) changed continuously, expanding and contracting over time. In each experiment, observers viewed the display and had to report the average size of the disc (or discs) over time.

Expt #2: Continuous averaging: Larger continuous average (1.1 MB)Expt #2: Continuous averaging: Smaller continuous average (1 MB)
To test whether observers are able to average in some sense continuously (and are not simply averaging the 9 'anchor points' between which the sizes are continuously changing in these displays, for example), we created two conditions that used identical sets of 9 'anchor points', but whose continuous average size over time was different. To do this, we divided each transformation into two halves and varied the amount of time each half took so that one half always took five times longer than the other. In the Larger Continuous Average condition, the longer half was always the one with the larger size (i.e. the first half for contractions but the second half for expansions). In the Smaller Continuous Average condition, the longer half was always the one with the smaller size (i.e. the first half for expansions and the second half for contractions). Observers reported larger average sizes in the Larger Continuous Average condition, despite the matched anchor points. This indicates that size averaging can operate in some sense continuously -- sampling multiple times during a single continuous transformation with no discrete boundaries.

Expt #3: Averaging and attentional capture: The larger items loom (116 KB)Expt #3: Averaging and attentional capture: The larger items recede (116 KB)
In this experiment we tested whether looming (expanding) and receding (contracting) objects differentially impact perceptual averaging, when both types of transformations were present in multi-object displays. We hypothesized that sampling occurs selectively (i.e. that objects will be sampled with a higher likelihood and/or more frequently) from expanding discs than from contracting discs, due to looming-induced capture. To test the automaticity of this effect, we employed a situation where such a bias would impair performance. Eight discs were presented simultaneously, and then each disc either expanded or contracted once (with all changes occuring at the same time). In the Larger Looming condition, the larger discs expanded while the smaller discs contracted. In the Larger Receding condition, the larger discs contracted while the smaller discs expanded. These two conditions were constructed so that each Larger Looming trial corresponded to a Larger Receding trial that had an identical continuous average size over time; in fact, each Larger Receding animation was identical to a Larger Looming animation played in reverse. Nevertheless, observers reported a larger average size in the Larger Looming condition, consistent with the idea the looming-induced attentional capture led to selective sampling from the expanding items during the averaging process.